[asy] /* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki File:3D template.png */ import three; defaultpen(linewidth(0.8)); real r=100; triple A=(0,0,0), B=(0,0,r), C=(0,r,r), D=(0,r,0), E=(r,r,0), F=(r,r,r), G=(r,0,r), H=(r,0,0); draw(F--A--B--C--D--A--E--B--F--G--H--E--H--G--C); draw(C--F--A--H,dashed); dot("$A$",A,SE); dot("$B$",B,SE); dot("$C$",C,N); dot("$D$",D,S); dot("$E$",E,NNW); dot("$F$",F,NE); dot("$G$",G,NE); dot("$H$",H,SE); [/asy]
Since triangular pyramid $CFAH$ is exactly half of rectangular prism $ABCDEFGH$, the ratio of their volumes is $\boxed{\frac{1}{2}}$.
Alternatively, if we denote the side length of the rectangular prism as 1, then the volume of $ABCDEFGH$ is 1, so the volume of tetrahedron $CFAH$ is $\frac{1}{6}$, so the volume of pyramid $CFAH$ is $\frac{1}{6}/\frac{1}{2}=\boxed{\frac{1}{3}}$.
Let $ABCDEFGH$ be a rectangular prism. Find the volume of pyramid $CFAH$.
1 answer